Course Description

AP Calculus AB stresses both conceptual understanding of calculus and fluency in mathematical procedures. The primary focus is on limits, derivatives, integrals, and the fundamental theorem of calculus. Students must be able to engage with graphical, numerical, analytical, and verbal representations of calculus concepts and demonstrate connections among them. Students develop the skills necessary to apply calculus in solving problems, and learn to view calculus as an elegant and yet eminently practical aspect of God’s creation. This course covers one and a half semesters of college calculus, and the content is similar to what students can expect on the AP exam. AP Calculus AB is approved for dual credit at Colorado Christian University.

Prerequisites

This is a rigorous, college-level course. We recommend students complete Algebra 2 and Pre-Calculus & Trigonometry before enrolling in AP Calculus AB. In particular, students need to understand the notion of functions and be familiar with trigonometric functions. Please visit the College Board’s website for a detailed list of topics students should be familiar with prior to taking the course and for more information about the AP exam. For help determining if your student is ready for this course, please use our self-graded AP Calculus AB Readiness Test.

Dual Credit

This course has been approved for dual credit at Colorado Christian University. Our AP Calculus AB course has been approved for equivalency with MAT 141 (Calculus I) with certain instructors.

If you are interested, please let us know at academy@hslda.org and follow the registration steps on Colorado Christian University’s Dual Credit flyer. Be sure to contact colleges or universities of interest to find out how the school will accept CCU transfer credits.

Students Will Learn

• How to understand the meaning of the derivate in terms of rate of change and local linear approximation
• How to understand the meaning of the definite integral as a limit of Riemann sums and as the net accumulation of change
• How to understand the relationship between the derivative and the definite integral as expressed in the fundamental theorem of calculus
• How to model a written description of a physical situation with a function, a differential equation, or an integral
• How to determine the reasonableness of solutions, including sign, size, relative accuracy, and units of measurement
• How to use technology to solve problems, experiment, interpret results, and verify conclusions
• How communicate mathematical solutions well both orally and in writing

AP^® Calculus AB is a rigorous, college-level course. The College Board recommends this course and the corresponding AP^® exam for advanced 11th grade students and up.

We estimate that the course workload will take 10+ hours per week. During a typical week in this course, students will complete the following coursework:

• 90 minutes of live class instruction
• 3 lecture videos
• 10-15 practice problems per lecture
• Discussion forum posts
• Quiz

Students complete an exam every four weeks and a final, mock AP exam at the end of the course.